Ostensibly, the answer is no. The architecture of most virtualisation platforms abstract the activity of the virtual 'guest' machine from that of the physical 'host' machine. There are, however, a couple of caveats to this:
Primarily, you are reliant of the security of your virtualisation platform, the major players (VMware, Microsoft hyper-V, Oracle) all have very good security track-records for host segregation, and I'm not aware of any publicised flaws. That said, the fact that the guest machine's processing and memory are still intrinsically based on the processor and memory of the host machine means that there could be exposure were flaws to exist in the software; this is however theoretical.
Host Tools. Most virtualisation platforms provide some form of tool/service which runs on the Guest OS and allows limited communication between the virtualisation service and the guest (e.g. VMware Tools). Again, whilst I am not aware of any identified flaws that could allow the breaking of the 'virtual curtain', it wouldn't be beyond the realms of possibility.
In this instance, I would suggest that you can get a very high level of assurance around the separation of your host and guest through the use of a current version of one of the major virtualisation platforms.
I hope that helps.